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lfunc_lfunctions • Show schema
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{'Lhash': '2118083825456253011226008028891', 'a10': [-3.2613872124741694, 1.8829627850535648], 'a2': [3.0590716208171305, 1.766155823749115], 'a3': [0.0, 0.0], 'a4': [4.23861278752583, 7.341492701605885], 'a5': [-0.5330681358161528, 0.9233010951296033], 'a6': [0.0, 0.0], 'a7': [0.47722557505166113, 0.0], 'a8': [0.0, 15.814956047231945], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 4.6594125205610775, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.0', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [19, [[1.0, 0], [6.522774424948339, 17.84526306338015]]]], 'bad_primes': [3, 19], 'central_character': '171.46', 'coefficient_field': 'CDF', 'conductor': 171, 'conductor_radical': 57, 'conjugate': '3466916130860755504681610294917', 'degree': 2, 'euler_factors': [[[1.0, 0], [-3.0590716208171305, -1.766155823749115], [2.0, 3.4641016151377544]], [[1.0, 0], [0, 0]], [[1.0, 0], [0.5330681358161528, -0.9233010951296033], [-12.5, 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[1740.5, 3014.634430573631]], [[1.0, 0], [35.8861278752583, 62.15659676686115], [-1860.5, 3222.4805274818964]], [[1.0, 0], [-7.624740662784136, 4.402146074159506], [2244.5, -3887.5880375883453]], [[1.0, 0], [-42.269653915120685, -24.404396066447244], [2520.5, 4365.634060477355]], [[1.0, 0], [56.79503017546495, -98.37187788131283], [-2664.5, -4615.049376767273]], [[1.0, 0], [-104.53364296299078, -60.352526904054955], [3120.5, 5404.864545018681]], [[1.0, 0], [65.44597750287183, 0], [6889.0, 0]], [[1.0, 0], [133.27862129666485, -76.94844788285164], [3960.5, -6859.787223376538]], [[1.0, 0], [83.09109769979335, 47.97266762423719], [4704.5, 8148.433024207783]], [[1.0, 0], [-13.5810971430604, -23.52315027430914], [-5100.5, 8834.325144005059]], [[1.0, 0], [0, 43.445308299696556], [-10609.0, 0]], [[1.0, 0], [0, -35.966687407063034], [-11449.0, 0]], [[1.0, 0], [70.04554884989668, 40.440816484022925], [5940.5, 10289.247822362915]], [[1.0, 0], [0, 19.99083862681091], [-12769.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 8, 'label': '2-171-19.8-c2-0-8', 'load_key': 'CMFs-workshop', 'motivic_weight': 2, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [2], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/171/3/p/f/46/4', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [3.252472451307542, 3.0797645662609137, 2.903684609012021, 2.721335518732886, 2.5292436836169916, 2.3238756584028875, 2.102152190953986, 1.8619214661165335, 1.6023634017753925, 1.3243047541164923, 1.030429177550929, 0.7253680106265699, 0.41565834383222805, 0.10955683976726122, -0.1832977771900133, -0.45237301522958856, -0.6868703869562536, -0.8764680992977639, -1.0121394671397173, -1.0869933232254705, -1.097070016120851, -1.0420176456600359, -0.9255698344806224, -0.7557501915502195, -0.5447408410265544, -0.3083734248318283, -0.06523039907991268, 0.16461925089232882, 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'10.53132334123534203489148791913396', '11.83362275136858106661015131783670', '12.17664227569489443543533581588870'], 'prelabel': '2-171-19.8-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.158567237905986, 'root_angle': -0.47603950664612127, 'root_number': '0.07520304377850638 - 0.9971682416756201*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.238019753323', 'prec': 50}, 'spectral_label': 'c2-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.67087352388340331862219089436', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.28428691420936871192945215184', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.33581256701005924747688623182', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 4.6594125205610775, 'bad_primes': [3, 19], 'central_character': '19.8', 'conductor': 171, 'conductor_radical': 57, 'degree': 2, 'index': 8, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/171/3/p/f/46/4'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': False, 'is_instance_G2Q': False, 'is_instance_HMF': False, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '2-171-19.8-c2-0-8', 'motivic_weight': 2, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [2], 'order_of_vanishing': 0, 'prelabel': '2-171-19.8-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.158567237905986, 'root_angle': -0.23801975332306063, 'self_dual': False, 'spectral_label': 'c2-0', 'z1': {'__RealLiteral__': 0, 'data': '1.67087352388340331862219089436', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2118083825456253011226008028891', 'Lhash_array': ['2118083825456253011226008028891'], 'label': '2-171-19.8-c2-0-8', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/171/3/p/f/46/4'}